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Re: CMP Connected Mathematics does not introduce Lowest Common
Denominator
Posted:
Dec 6, 2007 3:34 AM
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> "Misconceptions about Common Denominators
>
> Because common denominators are so important in
> computation with fractions, traditional school
> arithmetic has extensive teaching and practice in
> finding and using common denominators and
> especially in finding a "least common denominator
> (LCD) for two or more fractions. While some of this
> work is useful, the authors of EVERYDAY MATHEMATICS
> believe that it is usually overdone, too formal, and
> without much meaning for many people. In particular,
> the authors...
See, I don't think the authors really get it about
LCD. This is where supplementation for privileged
elites goes to Euclid's Algorithm, one of the oldest
known to computer science, breaking free of the silly
factor trees (which are OK, but way more work than
coding a 4 liner -- even on a TI (I think, not that
familiar with 'em)).
Why do we care about Euclid's Algorithm again? Don't
get me started, save to say I doubt the authors have
any intention of helping higher level teachers (still
pre college though) get through segments on RSA. That's
just not in their thinking. Meaning EM isn't in ours.
Some will say I don't know what I'm talking about
because Euclid's Algorithm is for GCD (greatest common
divisor) not LCD. But lcd(a,b) = (a*b)/gcd(a,b)
In Python:
IDLE 1.2.1
>>> def euclid(a,b):
while b:
a, b = b, a%b
return a
>>> def lcd(a,b):
return (a*b)/euclid(a,b)
>>> gcd = euclid
>>>
>>> gcd(51, 17*10)
17
>>> lcd(51, 170)
510
Note that a gcd algorithm comes in handy for testing
relative primality i.e. if gcd(a,b) is 1 then lcd is
simply both denominators multiplied. Relative primality
is intrinsic to "totient" concept which is how we get
to "clock arithmetic" (the modulo stuff). No, we don't
go as deeply as pro number theorists, but at least we
give kids some feel for what it's all about -- a little
relevance and realism makes math go a lot further, no?
Or is this ~M!
Kirby
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